# What is the first derivative test for critical points?

If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.

If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.

See Also:

https://tutor.hix.ai

By signing up, you agree to our Terms of Service and Privacy Policy

The first derivative test for critical points states that if a function ( f(x) ) has a critical point at ( x = c ):

- If ( f'(x) ) changes sign from negative to positive at ( x = c ), then ( f(c) ) is a local minimum.
- If ( f'(x) ) changes sign from positive to negative at ( x = c ), then ( f(c) ) is a local maximum.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If #f(x) = 2 sin x + sin 2x#, what are the points of inflection, concavity and critical points?
- How do you use the first and second derivatives to sketch # g(x)= ( 1 + x^2 ) / ( 1 - x^2 )#?
- How do you find the maximum, minimum and inflection points and concavity for the function #g(x) = 170 + 8x^3 + x^4#?
- How do you find all points of inflection for #f(x) = (1/12)x^4 - 2x^2 + 15#?
- How do you sketch the curve #f(x)=1+1/x^2# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7